Determine the magnitude of the electric field at a point located 4 cm away from a line charge with a density of 2 × 10^ -6 C m^ -1 .

Correct answer: B. 9 × 10^5 N C^ -1 The electric field due to an infinite line charge at a distance r is given by the formula: E = (λ)/(2 π _0 r) = (2kλ)/(r) Given: Linear charge density, λ = 2 × 10^ -6 C m^ -1 Distance, r = 4 cm = 4 × 10^ -2 m Coulomb's constant, k = 9 × 10^9 N m^2 C^ -2 Substituting the values into the formula: E = 2 × 9 × 10^9 × 2 × 10^ -6 4 × 10^ -2 E = 36 × 10^3 4 × 10^ -2 E = 9 × 10^5 N C^ -1

Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Gauss's Law

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Gauss's Law

Determine the magnitude of the electric field at a point located 4...

Determine the magnitude of the electric field at a point located

4 \text{ cm}

away from a line charge with a density of

2 \times 10^{-6} \text{ C m}^{-1}

Options

A $2.25 \times 10^7 \text{ N C}^{-1}$
B $9 \times 10^5 \text{ N C}^{-1}$
C $9 \times 10^3 \text{ N C}^{-1}$
D $4.5 \times 10^5 \text{ N C}^{-1}$

Correct answer

B. $9 \times 10^5 \text{ N C}^{-1}$

Step-by-step solution

The electric field due to an infinite line charge at a distance

r

is given by the formula:

E = \dfrac{\lambda}{2 \pi \epsilon_0 r} = \dfrac{2k\lambda}{r}

Given:
Linear charge density,

\lambda = 2 \times 10^{-6} \text{ C m}^{-1}

Distance,

r = 4 \text{ cm} = 4 \times 10^{-2} \text{ m}

Coulomb's constant,

k = 9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}

Substituting the values into the formula:

E = \dfrac{2 \times 9 \times 10^9 \times 2 \times 10^{-6}}{4 \times 10^{-2}}

E = \dfrac{36 \times 10^3}{4 \times 10^{-2}}

E = 9 \times 10^5 \text{ N C}^{-1}

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